If the change in the value of $‘g’$ at a height $h$ above the surface of the earth is the same as at a depth $x$ below it, then (both $x$ and $h$ being much smaller than the radius of the earth)

If $R$ is the radius of the earth and $g$ the acceleration due to gravity on the earth's surface, the mean density of the earth is

The ratio of the radius of the earth to that of the moon is $10$. The ratio of acceleration due to gravity on the earth and on the moon is $6$. The ratio of the escape velocity from the earth's surface to that from the moon is

The weight of an object in the coal mine, sea level, at the top of the mountain are ${W_1},\;{W_2}$ and ${W_3}$ respectively, then

The ratio of the weights of a body on the Earth's surface to that on the surface of a planet is $9 : 4$. The mass of the planet is $\frac{1}{9}^{th}$ of that of the Earth. If $'R'$ is the radius of the Earth, what is the radius of the planet ? (Take the planets to have the same mass density)